A PRINCIPAL TOPOLOGY OBTAINED FROM UNINORMS

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Karaçal F., Köroğlu T.

KYBERNETIKA, vol.58, no.6, pp.863-882, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 58 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.14736/kyb-2022-6-0863
  • Journal Name: KYBERNETIKA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Linguistic Bibliography, zbMATH
  • Page Numbers: pp.863-882
  • Keywords: uninorm, closure operator, principal topology, bounded lattice, OPERATORS, SET
  • Karadeniz Technical University Affiliated: Yes

Abstract

We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a bounded lattice based on equality of the topologies induced by uninorms.